Question

For the data set below, compute the standard deviation. Round to the nearest hundredth. 2, 3, 5, 8 2.03 2.20 2.6 4.5

Answer 1

$The \ standard \ deviation = \sqrt{ \frac{1}{n} \sum ( x_{i} - \mu )^2 } \\ where: \\ n \ is\ the \ number \ of \ elements \\ x_{i} \ element \ number \ i \\ \mu \ is \ the \ mean \ of \ the \ elements$

The elements are :
                                2,3,5,8,2.03,2.20,2.6,4.5
n = 8

μ = ( 2 + 3 + 5 + 8 + 2.03 + 2.20 + 2.6 + 4.5 )/8 = 3.66625

sum = ( 2 - 3.66625)² + ( 3 - 3.66625)² + ( 5 - 3.66625)² + ( 8 - 3.66625)² +
( 2.03 - 3.66625)² + ( 2.20 - 3.66625)² + ( 2.6 - 3.66625)² + ( 4.5 - 3.66625)²
      = 30.44

∴ The standard deviation = √ (30.44 / 8)
                                         ≈ 1.95 ( to the nearest hundredth )